How do I get rid of intersecting vertices between two gameobjects?

Hello, I am trying to make this little project about a cell that you are able to edit. The way the player can edit cell by inserting different pieces of mass to create the cells shape and form giving the player freedom. However whenever the two objects meet, aka, when mass is added to the cell, there is another object created in between them and its definitely not visually appealing. How am I able to get rid of the intersecting object so that when I add mass it looks like that both the cell and mass look like one object. I know this is very complicated but does anyone know any documentation on this. Thank you in advance.